Varieties of groupoids with comprehensive free products
type: Item
instance of: scholarly article
title: Varieties of groupoids with comprehensive free products
zbMATH Open document ID: 0604.20057
DOI: 10.1007/BF01224020
author: B. George
published in: Algebra Universalis
publication date: 1986-01-01T00:00:00Z
review text: A variety \(V\) has comprehensive free products if, for every integer \(m\geq 3\) there is a countable algebra \(A\in V\) such that \(A\) is isomorphic to the \(V\)-free product of \(m\) copies of \(A\), but \(A\) is not isomorphic to the \(V\)-free product of \(k\) copies of \(A\) for \(1<k<m\). The authors prove that the following varieties have comprehensive free products: the variety of all semigroups, any variety of commutative semigroups containing all semilattices, the varieties of groupoids, commutative groupoids, idempotent groupoids and commutative idempotent groupoids. They point out that this question, for the variety of idempotent semigroups, is still open.
Mathematics Subject Classification ID: 20M07
Mathematics Subject Classification ID: 20L05
Mathematics Subject Classification ID: 08B25
zbMATH DE Number: 3975230
zbMATH Keywords: comprehensive free products
zbMATH Keywords: variety of commutative semigroups
zbMATH Keywords: varieties of groupoids
zbMATH Keywords: commutative idempotent groupoids
MaRDI profile type: Publication
cites work: Isomorphisms of sums of countable bounded distributive lattices
cites work: Q5564342
cites work: Lattices isomorphic with their free powers
cites work: Relatively free products in regular varieties
cites work: The structure of countable Boolean algebras
cites work: Isomorphisms of Sums of Countable Boolean Algebras
full work available at URL: https://doi.org/10.1007/bf01224020
OpenAlex ID: W2028911489
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description: scientific article; zbMATH DE number 3975230